All three email drafts successfully accomplish the core goal: politely requesting explicit confirmation from LSE Admissions whether your daughter's decision is a final rejection or reserve-list placement. Each includes the essential identification details (applicant name, UCAS ID, programme, date of birth) needed for a timely response, and each maintains the respectful, professional tone appropriate for institutional communication.

The three drafts differ primarily in scope and conciseness rather than substance. The first draft is the most concise, asking a straightforward single question about reserve-list status without additional context. The second draft provides slightly more framing by acknowledging that reserve-list status should be explicitly communicated, which may help the admissions office understand why clarification is needed. The third draft is the most comprehensive, explicitly asking for timeline and next steps if she is on a reserve list, and requesting confirmation of finality if she is not—this gives the admissions team clearer guidance on what information would be most helpful.

For your situation, choose based on your preference: if you want brevity and directness, use the first; if you prefer a middle ground with helpful context, use the second; if you want to maximize the usefulness of the response by explicitly requesting timeline information, use the third. All three are appropriate for a parent to send on behalf of the applicant. Send only one email to avoid appearing to press the issue, and expect a response within a few working days during the busy admissions period. The key point is that one polite, single inquiry with clear applicant details is entirely reasonable and should receive a definitive answer.